FFT

Q

• 变换(Transform) -> 傅里叶变换(Fourier Transform) -> 傅里叶级数(Fourier Series) -> 傅里叶快速变换(Fast Fourier Transform)
• FFT 和 DFT 有啥区别？
• FFT 目前的主流实现方式有哪些(Cooley-Tukey algorithm)？速度最快的方式？代码空间最省的方式？

Tutorial

• 傅里叶分析之掐死教程（完整版）更新于2014.06.06
• What Makes a Fourier Transform Fast?
• http://www.katjaas.nl/fourier/fourier.html
• FFT Tutorial
• Fast Fourier Transform and MATLAB Implementation
• Cooley–Tukey FFT algorithm Wikipedea
• Fast Fourier Transform and MATLAB Implementation
• How to Interpret FFT results – complex DFT, frequency bins and FFTShift
• How to Interpret FFT results – obtaining Magnitude and Phase information
• FFT and Spectral Leakage
• How to plot FFT using Matlab – FFT of basic signals : Sine and Cosine waves
• Generating Basic signals – Square Wave and Power Spectral Density using FFT
• Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
• Generating Basic Signals – Gaussian Pulse and Power Spectral Density using FFT
• Chirp Signal – Frequency Sweeping – FFT and power spectral density
• Constructing the Auto Correlation Matrix using FFT

Paper

• An algorithm for the machine calculation of complex Fourier series

Example

• Fast Fourier transform : Calculate the FFT (Fast Fourier Transform) of an input sequence.

Library

• FFTW : FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). We believe that FFTW, which is free software, should become the FFT library of choice for most applications.
• FFTSS : FFTSS is an open source library for computing the Fast Fourier Transform. Since FFTW is already the de facto standard FFT library, we made the interfaces of this library almost compatible with those of FFTW. This makes it easy to run your applications coded for FFTW.
• KISS FFT : a Fast Fourier Transform (FFT) library that tries to Keep it Simple, Stupid